加入具雙凹面中間桿的平移式從動件之盤形凸輪機構的設計

The Design of Disk Cam Mechanisms with a Translating Follower Having an Added Dual-concave-faced Intermediate Link

許家榮

指導教授 ： 吳隆庸

國立清華大學/工學院/動力機械工程學系/碩士(2013年)

https://doi.org/10.6843/NTHU.2013.00308

摘要

本研究提出一套解析法來設計額外加入具雙凹面中間桿的平移式從動件之盤形凸輪機構。當凸輪和它的從動件受力而互相接觸時，它們實際的接觸面積非常小，因此接觸應力會相當高。從動件的配置方式會影響凸輪與從動件之間的接觸應力，根據赫茲接觸應力理論，兩圓柱體間的接觸應力會受到正向力及圓柱體的曲率半徑影響。本研究提出一種改良式之新配置的從動件以降低接觸應力；也就是在習用的從動件與凸輪之間額外加入一個具雙凹面的中間桿件。此新型配置的目的是產生以凸面對凹面的形式，且隨時都會和凸輪保持接觸的兩個接觸點來有效地增加凸輪與從動件之間的接觸面積，從而得以相對降低其接觸應力。
首先，對平移式單凹面從動件將它的運動曲線加以適當補償性調整，再利用瞬心向量法設計一個對應的凸輪輪廓。這個凸輪輪廓將會非常平滑而被採用為替代的凸輪，並用以驅動上述提出的改良式之新配置的從動件。因為對應於原始單凹面從動件的運動曲線已加以適當補償性調整，所以採用此替代的凸輪來驅動時將可以使這個從動件在運動周期中達成預定的暫停區間以及升程量。這個替代凸輪的輪廓和中間桿件之雙凹面的接觸點可以依照凸輪輪廓的幾何條件決定，藉此即可進一步求得從動件的升程運動曲線以及降程運動曲線。將凸輪機構受力狀態分析之後，即可用赫茲接觸應力理論計算凸輪與雙凹面的接觸應力，並將所得到的結果及現象和平移式單凹面從動件之凸輪機構的接觸應力加以比較。本文並進一步分析採用非對稱運動曲線以及調整機構的各個設計參數對凸輪與從動件之間接觸應力的影響。相對於平移式平面從動件，透過此新型從動件的應用，凸輪與從動件之間的接觸應力可降低33.74%。

關鍵字

雙凹面 ； 凸輪連桿機構 ； 凸輪輪廓 ； 接觸應力

並列摘要

The work presents an analytical approach for designing disk cam mechanisms with a translating follower having an extraneously added dual-concave-faced intermediate link. When the cam and its follower are pressed into contact, high contact stresses may occur due to very small actual contact area. The arrangement of the follower can affect the contact stress between the cam and the follower. According to the Hertz theory, the contact stress between two cylinders is affected by the normal force and the cylinder radius curvatures. This work proposes a modified arrangement of the common translating follower to reduce the contact stress. That is, an extraneous intermediate link having dual-concave faces is added between the cam and the common follower. Introducing this novel arrangement is intended to result in two convex-to-concave contact points so as to significantly increase the actual contact area.
As a first step, the profile of the cam with a translating single-concave-faced follower having a compensatively adjusted motion curve is calculated by applying the concept of velocity instant center. The obtained cam profile is then employed as a substitute cam to drive the presented novel follower. Because the motion curve of the original common follower has been compensatively adjusted, the presented novel follower driven by this substitute cam profile can achieve the expected dwells and the expected total rise during the motion cycle. The contact points between the substitute cam and the dual-concave faces of the intermediate link are determined according to the profile geometries of the substitute cam. The rise motion curve and the fall motion curve of the presented novel follower driven by this substitute cam profile is analyzed. After a force analysis of the cam mechanism has been undertaken, the Hertz contact stress theory is applied to determine the caused contact stresses; the results are compared with those of disk cam mechanisms with single-concave-faced follower. Then, the effect of each design parameter as well as the asymmetric factors of the follower motion curve on the induced contact stress is analyzed. Finally, it is found that through the application of this novel follower, the contact stress can be reduced by 13% to 22%.

並列關鍵字

dual-concave faces ； cam-modulated linkage ； cam profile ； contact stress

參考文獻

[4]陳端偉，2008，平移式凹面從動件之盤形凸輪機構設計與分析，碩士論文，國立清華大學動力機械工程學系，新竹。

[5]Wu, L. I., Liu, C. H., Shu, K. L., and Chou, S. L., 2009, “Disk cam mechanisms with a translating follower having symmetrical double rollers,” Mechanism and Machine Theory, Vol. 223, No. 6, pp. 1443-1448.

[6]周孫良，2008，平移式雙滾子從動件之盤形凸輪機構設計與分析，碩士論文，國立清華大學動力機械工程學系，新竹。

[7]劉俊賢，2011，盤形凸輪機構之新類型從動件的設計，博士論文，國立清華大學動力機械工程學系，新竹。

[10]Rothbart, H. A., Cam Design Handbook, McGraw-Hill, NewYork, pp. 222-223.